Stability analysis of three-dimensional breather solitons in a Bose-Einstein Condensate

We investigate the stability properties of breather soliton trains in a three-dimensional Bose-Einstein Condensate with Feshbach Resonance Management of the scattering length. This is done so as to generate both attractive and repulsive interaction. The condensate is con ned only by a one dimensional optical lattice and we consider both strong, moderate, and weak con nement. By strong con nement we mean a situation in which a quasi two dimensional soliton is created. Moderate con nement admits a fully three dimensional soliton. Weak con nement allows individual solitons to interact. Stability properties are investigated by several theoretical methods such as a variational analysis, treatment of motion in e ective potential wells, and collapse dynamics. Armed with all the information forthcoming from these methods, we then undertake a numerical calculation. Our theoretical predictions are fully con rmed, perhaps to a higher degree than expected. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi two-dimensional treatment, when the dynamics in one direction are frozen. We nd that in the 3D case the stability region splits into two parts. However, as we tighten the con nement, one of the islands of stability moves toward higher frequencies and the lower frequency region becomes more and more like that for quasi 2D. We demonstrate these solutions in direct numerical simulations and, importantly, suggest a way of creating robust 3D solitons in experiments in a Bose Einstein Condensate in a one-dimensional lattice.Comment: 14 pages, 6 figures; accepted to Proc. Roy. Soc. London

Raman scattering of atoms from a quasi-condensate in a perturbative regime

It is demonstrated that measurements of positions of atoms scattered from a quasi-condensate in a Raman process provide information on the temperature of the parent cloud. In particular, the widths of the density and second order correlation functions are sensitive to the phase fluctuations induced by non-zero temperature of the quasi-condensate. It is also shown how these widths evolve during expansion of the cloud of scattered atoms. These results are useful for planning future Raman scattering experiments and indicate the degree of spatial resolution of atom-position measurements necessary to detect the temperature dependence of the quasi-condensate.Comment: 8 pages, 8 figure

Bogoliubov theory for atom scattering into separate regions

We review the Bogoliubov theory in the context of recent experiments, where atoms are scattered from a Bose-Einstein Condensate into two well-separated regions. We find the full dynamics of the pair-production process, calculate the first and second order correlation functions and show that the system is ideally number-squeezed. We calculate the Fisher information to show how the entanglement between the atoms from the two regions changes in time. We also provide a simple expression for the lower bound of the useful entanglement in the system in terms of the average number of scattered atoms and the number of modes they occupy. We then apply our theory to a recent "twin-beam" experiment [R. B\"ucker {\it et al.}, Nat. Phys. {\bf 7}, 608 (2011)]. The only numerical step of our semi-analytical description can be easily solved and does not require implementation of any stochastic methods.Comment: 11 pages, 6 figure

Phase separation of binary condensates in harmonic and lattice potentials

We propose a modified Gaussian ansatz to study binary condensates, trapped in harmonic and optical lattice potentials, both in miscible and immiscible domains. The ansatz is an apt one as it leads to the smooth transition from miscible to immiscible domains without any {\em a priori} assumptions. In optical lattice potentials, we analyze the squeezing of the density profiles due to the increase in the depth of the optical lattice potential. For this we develop a model with three potential wells, and define the relationship between the lattice depth and profile of the condensate.Comment: 13 pages, 11 figures, additional references adde